Startups, Small Businesses, and Large Companies

One of the reasons I like my Production Function Space (PFS) hypothesis, is that it clarifies a lot of issues that have puzzled me for a while. For example, as part of my work on seed-stage startup investing with RSCM, I have struggled with two questions: (1) what’s the difference between a startup and a small business and (2) why do some large companies have initiatives like venture groups and startup incubators?

To answer these questions, I’m going to have to get a little mathematical. Don’t worry. No derivatives or integrals, but I need to introduce some notation to keep the story straight. First, let’s define production footprint and search area.

A production footprint is the surface that encloses a set of points in PFS.* If A is a production function for basketballs, B is a production function for baseballs, and C is a production function for golfballs, then pf(ABC) looks like this in two dimensions:

We can also talk about the production footprint of a company like Google. pf(Google) is the surface that encloses all the production functions that Google currently uses.

A search area is the surface defined by extending the production footprint outward by the search radius.** Imagine that we wanted to see if making basketballs, baseballs, and golfballs would enable a company to make footballs using production function F, we might want to compute sa(r, ABC). It looks like this in two dimensions:

We can also talk about search areas for a company. sa(r,Google) is the surface enclosing all the points in PFS within r units of Google’s current production footprint. If we write just sa(Google), we mean search area using Google’s actual search radius.

With these two basic concepts in place, I can now easily answer questions (1) and (2). SU stands for startup, SB stands for small business, and LC stands for large company. So what’s the difference between a startup and a small business? Well, when they are founded, a startup doesn’t have any production footprint at all and a small business does. To a first order, pf(SU)=0 and pf(SB)>0. A startup doesn’t know with any precision how it’s going to make stuff. A small business does. Whether it’s a dry cleaner, law office, or liquor distributor, the founders know pretty precisely what they’re going to do and how they’re going to do it. However, startups have a much larger search radius than small businesses. r(SU)>r(SB). Assuming that we can define a search area on a set of production functions the startup could currently implement (but hasn’t yet), I content that also sa(SU)>sa(SB).

This realization was an epiphany for me. Even though the average person thinks of startups and small businesses as similar, they are actually polar opposites. They may both have a few employees working in a small office, but one is widely focused on exploring a huge region of PFS while the other is narrowly focused on implementing production functions within a tiny region of PFS. I also realized that you need to evaluate two things in a startup: (a) its ability to search PFS and (b) the ability to implement a production function once it locates a promising region of PFS. But the magnitude of impact for (a) is at least as big as (b) in the very early stages.

Now on to the issue of large companies. The problem here is search costs. Remember that, in three-dimensional space, volume increases as the cube of distance. In PFS, volume increase as an exponent of distance equal to the dimensionality of PFS. I posit that PFS is high-dimension, so this volume increases very quickly indeed. Now try to visualize the production footprint and search area of a large company. A large company has a lot of production functions in play so pf(LC) is large. But sa(r,LC) increases exponentially from this large volume by a large exponent.

In three dimensions, imagine that pf(LC) is like a hot air balloon. Extending just 10 feet out from the hot air balloon’s surface encompasses a huge volume of additional air. But in high-dimension PFS, the effect is… well… exponentially greater. So a large company has a problem. On the one hand, increasing its search radius is enormously costly. On the other hand, we know that Black Swan shifts in the fabric of PFS will occasionally render a huge volume dramatically less profitable, probably killing companies limited to that volume. So it’s only a matter of time before sa(r,LC) is hit by one of these shifts, for any value of r.

Internal venture groups and incubators represent a hack that attempts to circumvent this cold, hard calculation. The problem is that it’s difficult to explore a region of PFS without actually trying to implement a production function in that region. Sure, paper analysis and small experiments buy you some visibility, but not very much. Also, in most cases, you don’t get very good information from other firms on their explorations of PFS, unless you observe a massive success or failure, at which point it’s too late to do much about your position. That’s why search costs are so darn high. Enter corporate venture groups and startup incubators.

These initiatives require some capital investment by the large company. But this investment is then multiplied by the monetary capital of other investors as well as the human capital of the entrepreneurs. With careful management, a large company can get almost as much insight into explorations of PFS by these startups as it would from its own direct efforts. Moreover, because startups are willing to explore PFS farther from existing production footprints, the large company actually gets better search coverage of PFS.

This framework answers a key question about such initiatives. To what extent should corporate venture groups and startup incubators restrict the startups they back to those with a “strategic” fit”? If you believe in my PFS hypothesis, the answer is close to zero or perhaps even less than zero (look for startups in areas outside your company’s area of expertise). Otherwise, they’re biasing their searches to the region of PFS that’s close to the region they’re already searching. It doesn’t increase the ability to survive that much. As far as I know, Google is the only company that adopts this approach. I think they’re right and now I think I understand why. Epiphany number three.

* There are some mathematical details here that need to be fleshed out to define this surface. But I don’t think they add to the discussion and my topology is really rusty.

** More mathematical details omitted. The only important one is that the extension outward doesn’t have to be by a constant radius. It can be a function of the point on the pf. In that case, r is a global scaling parameter for the function.

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14 Responses

To what degree do you think it makes sense for there to be a continuum between idealized startups and idealized small business? My inclination has been toward having a positive production footprint (at least enough to pay the bills) and a large search area.

This is an excellent question. I think it’s pretty bi-modal in practice. Well-understood, small-scale production functions tend to be competitive. Thus there’s likely to be little surplus from implementing one to support a co-located group of folks exploring distant regions of PFS.

The one exception is if an SU/SB can extract monopoly rents from an existing production function. The obvious example here is consulting where some of the principles have rare skills. But I suppose there could be other highly distinctive products or services where an SU/SB could have some monopoly power.

Even so, I posit that there are increasing returns to scale in searching PFS at low levels of effort. There’s a critical mass to being able to get something useful done. Taking away from that critical mass to “pay the bills” may do more harm than good even if you can extract monopoly rents. Could go either way.

But if your bill paying production function doesn’t generate some substantial surplus, it’s definitely not a good idea.

I agree with Kevin. Any capital spent paying the bills reduces future EV. Entrepreneurs are often obsessed with making sure the lights stay on, but forget that their ingenuity is quite applicable to all aspects of their life. E.g. Why spend on rent when you can live with parents or couch surf?

It’s could be true in general that capital spent paying bills reduces future EV. But it seems possible to be engaged in something (to pay bills) that stimulates higher quality search. Also, if you exchange too large a share of your future EV so that you don’t ‘waste time’ working to pay the bills, you will wind up with less.

I understand. I am suggesting that necessity-being-the-mother-of invention is not taken seriously as a strategic choice and it should be, given our bias towards linear extrapolation of the future.

The poker analogy is: you are saying be cautious about going broke in a tournament because your EV goes down if you are unable to apply your edge (bias towards survival). I’m saying, just outside the casino the entire world has morphed into something unpredictable with a richer utility space than the known unknowns on the felt. A new tournament is about to start with all the bad busted players; your grandma just showed up in a red Ferrari to whisk you to the goldmine on her property in Pahrump that has been fallow up til today when she struck the motherlode; George Soros watched watched you play your last hand so creatively and aggressively that even though you busted out, he was inspired to approach you about his new hedge fund strategy. Etc.

In other words, life — and entrepreneurship — is what happens when you are making other plans.

I understand. I am suggesting that necessity-being-the-mother-of invention is not taken seriously as a strategic choice and it should be, given our bias towards linear extrapolation of the future.

The poker analogy is: you are saying be cautious about going broke in a tournament because your EV goes down if you are unable to apply your edge (bias towards survival). I’m saying, just outside the casino the entire world has morphed into something unpredictable with a richer utility space than the known unknowns on the felt. A new tournament is about to start with all the bad busted players; your grandma just showed up in a red Ferrari to whisk you to the goldmine on her property in Pahrump that has been fallow up til today when she struck the motherlode; George Soros watched watched you play your last hand so creatively and aggressively that even though you busted out, he was inspired to approach you about his new hedge fund strategy. Etc.

In other words, life — and entrepreneurship — is what happens when you are making other plans.

In other words startups have no PFs and achieve goods by pure production, but they forget that any real profitability comes from the often difficult creation of a PF. The skills and mindset to produce are different than those to produce PFs.

I see The Idea as simply the point at which the startup will start the search of PFS. But startups search PFS far away from currently explored regions so we have very little good information about which starting points are better than others. So what we’re really betting on is the ability to explore.

[…] I used my Production Function Space (PFS) hypothesis to illuminate the differences between startups, small businesses, and large companies. Now, I’d like to turn my attention to the implications of PFS on a firm’s demand for […]